13th International Conference on Membrane Computing - MTA Sztaki

F. Ipate, C. Dragomir, R. Lefticaru, L. Mierla, M.J. Pérez-Jiménez
defined across the two compartments.
A rule can have one the following types:
– (a) rewriting and communication rule: x → y {g},
where x ∈ A + , y ∈ A ∗ , g ∈ F E(A ∪ Ā); the right hand side, y, has the form
y = (a 1 , t 1 ) . . . (a h , t h ), where a j ∈ A and t j ∈ L, 1 ≤ j ≤ h, is an object and
a target, i.e., the label of a compartment, respectively; the target, t j , must be
either the label of the current compartment, l i , (more often ignored) or of an
existing neighbour of it ((l i , t j ) ∈ E) or an unspecified one, ∗; otherwise the
rule is not applicable; if a target, t j , refers to a label that appears more than
once then one of the involved compartments will be non-deterministically
chosen; if t j is ∗ then the object a j is sent to a neighbouring compartment
arbitrarily chosen;
– (b) input-output rule, is a form of symport/antiport rule: (x/y) {g},
where x, y ∈ A ∗ , g ∈ F E(A ∪ Ā); x from the current region, l i, is sent to the
environment and y from the environment is brought into the current region;
– (c) system structure rules; the following types are considered:
• (c1) membrane division rule: [] li → [] li1 . . . [] lih {g},
where g ∈ F E(A ∪ Ā); the compartment l i will be replaced by h compartments
obtained from l i , i.e., the content of them will coincide with
that of l i ; their labels are l i1 , . . . , l ih , respectively; all the links of l i are
inherited by each of the newly created compartments;
• (c2) membrane dissolution rule: [] li → λ {g};
the compartment l i will be destroyed together with its links;
• (c3) link creation rule: [] li ; [] lj → [] li − [] lj {cg};
the current compartment, l i , is linked to l j and if more than one l j
exists then one of them will be non-deterministically picked up; cg, called
compound guard, describes an expression l i .g 1 op l j .g 2 as defined above;
• (c4) link destruction rule: [] li − [] lj → [] li ; [] lj {cg};
is the opposite of link creation and means that compartments l i , l j are
disconnected; as usual, when more than a link, (l i , l j ) ∈ E, exists then
only one is considered by this rule; cg is a compound guard.
Further details and examples of kP system computations can be found in [5].
2.2 Regular Expressions and their Interpretation for kP Systems
In kP systems the rule execution strategy is described using regular expressions
over the sets of labels of rules.
First consider the set of labels of the rules from the set R in a given compartment,
denoted by Lab(R). The set of regular expressions over this set is denoted
by REG(Lab(R)). A regular expression σ ∈ REG(Lab(R)) is interpreted as
follows:
– σ = ɛ means no rule from the current compartment will be executed;
– σ = r, r ∈ Lab(R), means the rule r is executed;
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